Ammonia, nitrite and nitrate are all clear chemicals so you wouldn't see them in your tank. It's not recommended to use extra chemicals in your axolotl tank as they absorb substances through their skin and can easily be poisoned by most fish and reptile safe treatments. Seachem Prime can be used to lessen the toxicity of nitrites and ammonia during spikes or cycle crashes while you do water changes to get it under control.
Cloudy water could be a bacteria bloom or debris from sand substrate that wasn't fully washed before it was added to the tank. Algae can and probably will grow on your tank walls as your tank matures. This can make it appear like the water is cloudy as well. You can remove the algae build up with an aquarium scrape or rag/paper towel when you do water changes. Just be aware that the algae will fall back into the water so be careful or have a decent filter. It's not recommended to buy algae eating fish or shrimp to put in the tank as they could harm the axolotl if they decided to eat one.
My advice would be to buy a liquid freshwater aquarium test kit to monitor the nitrogen cycle in your tank. I'm not sure if you've cycled it, if not be prepared to do some water changes daily to prevent dangerous levels of ammonia and nitrite from building up.
But the cloudiness will die down as the aquarium settles. If not, partial water changes would be necessary.
There are lots of other threads on bacteria blooms and such on the forum I'm sure you'll find some useful information there.